x$($a$)$ The Russell Paradox A logical difficulty arises from the idea, which

at first appears natural, of calling any collection of objects a set. Let$$s

say that set B is ordinary if B $$ B$.$ For example, if B is the set of all

chairs, then B $$ B$,$ because B is not a chair. It is only in the case of very

unusual collections that we are tempted to say that a set is a member of

itself. $($The collection of all abstract ideas certainly is an abstract idea.$)$

Let X $=\{$x: x is an ordinary set$\}.$ Is X $$ X$?$ Is X $$ X$?$ What should we

say about the collection of all ordinary sets?

$($b$)$ In the town of Seville, the $($male$)$ barber shaves all the men, and only

the men, who do not shave themselves. Let A be the set of all men in the

town who do not shave themselves. Who shaves the barber? $($That is$,$ is

the barber an element of A$?$ Is he not an element of A$?)$